Repeat Problem 16.18 using the generalized charts, instead of ideal gas behavior.

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Accepted Answer

[latex]\begin{aligned}& \left( Z _1- Z _2 ight)=5000 \,m , \quad P _1=15 \,MPa \& T =40^{\circ} C = const \& T _{ r }=\frac{313.2}{304.1}=1.03, \quad P _{ r 1}=\frac{15}{7.38}=2.033 \& ext { Equilibrium: } \quad- w _{ REV }=0=\Delta g +\Delta PE\end{aligned}[/latex]

[latex]g _2- g _1= h _2- h _1- T \left( s _2- s _1 ight)= g \left( Z _1- Z _2 ight)=\frac{9.807 imes 5000}{1000}=49.04 \,kJ / kg[/latex]

From Figures D.2 and D.3,

[latex]\begin{aligned}& h _1^*- h _1= RT _{ c } imes 3.54=203.4 kJ / kg ; \quad s _1^*- s _1= R imes 2.61=0.4931 \,kJ / kg K \& h _2^*- h _1^*=0 ; \quad s _2^*- s _1^*=0- R \ln \left( P _2 / P _1 ight)=0.18892 \ln \left( P _2 / 15 ight)\end{aligned}[/latex]

Trial and error. Assume [latex]P _2=55 MPa \quad\left( P _{ r 2}=55 / 7.38=7.45 ight)[/latex]

[latex]\begin{gathered}h _2^*- h _2= RT _{ c } imes 3.60=206.8 kJ / kg ; \quad s _2^*- s _2= R imes 2.14=0.4043 \,kJ / kg K \\Delta g =-206.8+0+203.4-313.2[-0.4043-0.18892 \ln (55 / 15)+0.4931]=45.7\end{gathered}[/latex]

Too low so assume [latex]P _2=60 \,MPa \quad\left( P _{ r 2}=60 / 7.38=8.13 ight)[/latex]

[latex]\begin{gathered}h _2^*- h _2= RT _{ c } imes 3.57=205.1 kJ / kg ; \quad s _2^*- s _2= R imes 2.11=0.3986\, kJ / kg K \Δg =-205.1+0+203.4-313.2[-0.3986-0.18892 \ln (60 / 15)+0.4931]=50.7 \ ext { Make linear interpolation } \Rightarrow P _2= 5 8 ~ M P a\end{gathered}[/latex]

Question 16.CSGP.104: Repeat Problem 16.18 using the generalized charts, instead o......

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